erweitern ((x^2+5x+9)^n+x^2(x+5)^2+2)/(x^2+5x+8)

Lösung

erweitern

\frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{2} ( x + 5 ) ^{2} + 2}{x ^{2} + 5 x + 8}

\frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{4} + 10 x ^{3} + 25 x ^{2} + 2}{x ^{2} + 5 x + 8}

Schritte zur Lösung

\frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{2} ( x + 5 ) ^{2} + 2}{x ^{2} + 5 x + 8}

(x + 5)^{2} = x^{2} + 10 x + 25

= \frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{2} ( x ^{2} + 10 x + 25 ) + 2}{x ^{2} + 5 x + 8}

Multipliziere aus

(x^{2} + 5 x + 9)^{n} + x^{2} (x^{2} + 10 x + 25) + 2 : (x^{2} + 5 x + 9)^{n} + x^{4} + 10 x^{3} + 25 x^{2} + 2

= \frac{( x ^{2} + 5 x + 9 ) ^{n} + x ^{4} + 10 x ^{3} + 25 x ^{2} + 2}{x ^{2} + 5 x + 8}

e x p an d x ((x - 1) (x - 2))

\frac{d}{d t} ((t) (k (M - t)))

e x p an d \frac{2 x ^{5} + x ^{4} + 4 x ^{3} + 3 x ^{2} - 24 x}{( x ^{2} + 1 ) ^{2}}

e x p an d \frac{3 x ^{2} ( 3 x ^{2} + 2 x ^{4} )}{8}

e x p an d \frac{( s + 2 )}{( s ^{2} + 4 s + 3 ) \cdot ( s + 5 )}